Galula's Counterinsurgency Warfare (chap. 4, pp.43-47) uses "Revolutionary" for "X" - insert whatever word suits your fancy.

The situation is one where the insurgent's acts are generally legal and non-violent - ranging up to the situation where military forces have to take an active role because of violence that police actions cannot control.

The counterinsurgent has 4 methods in a "cold war":

1. Direct police and legal action vs. the insurgents (primarily directed at its infra-structure).

2. Indirect action by alleviating the underlying conditions supporting the insurgency's cause.

3. Infiltration of the insurgency (intelligence & derailment).

4. Co-opt the insurgency into a mainstream political movement.

Now, moving to Bob's World's example of the Civil Rights Movement, which addresses only one side of the coin (pun intended) - Black Voting Rights, etc. One can cite use of all four methods by local, state and Federal authorities in that era; but the Kennedy-Johnson approach was to emphasize #2 (enforcement of the Civil Rights Acts) and #4 (bringing Black voters into the Democratic Party, realizing that substantial numbers of White voters would be lost).

The other insurgency was the anti-Civil Rights movement, which had both non-violent and violent aspects. Once the decision was made to pursue enforcement of the Civil Rights Acts, application of method #2 in favor of the "antis" was not possible - although as time went on (now 5 decades), modifications were made to satisfy some of the concerns about busing, affirmative action, etc.

The methods used against the "antis" tending to violence were largely #1 and #3 (e.g., Mississippi Burning). That again was a long process; and there were still a large number of dissatisfied Whites without a political home. That need was met by Nixon's Southern Strategy, which changed the US political map by bringing former Democrats into the Republican Party. That message (method #4) was conveyed in a number of ways - including SCOTUS nominations of two Southern judges (Haynsworth & Carswell in 1969 & 1970), which were destined to fail from the gitgo.

The foregoing is an explanation by hindsight - the various responses developed because of the US system of governance - not because of some magical 50-year plan.